Updating intensities in a phd filter based on a sensor track id

ABSTRACT

In one embodiment, a method of tracking multiple objects with a probabilistic hypothesis density filter is provided. The method includes obtaining measurements corresponding to a first object with at least one sensor, the at least one sensor providing one or more first track IDs for the measurements. A T k+1  first predicted intensity is generated for the first object based on a T k  first track intensity. A T k+1  measurement from a first sensor of the at least one sensors is obtained, the first sensor providing a second track ID for the T k+1  measurement. The second track ID is compared to the one or more first track IDs, and the T k+1  first predicted intensity is selectively updated with the T k+1  measurement based on whether the second track ID matches any of the one or more first track IDs to generate a T k+1  first measurement-to-track intensity for the first object.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to the following co-pending United States patent applications, which are hereby incorporated herein by reference:

U.S. patent application Ser. No. ______ (Attorney Docket No. H0043916) entitled “MERGING INTENSITIES IN A PHD FILTER BASED ON A SENSOR TRACK ID” filed on even date herewith;

U.S. patent application Ser. No. ______ (Attorney Docket No. H0045529) entitled “ADJUSTING WEIGHT OF INTENSITY IN A PHD FILTER BASED ON SENSOR TRACK ID” filed on even date herewith; and

U.S. patent application Ser. No. ______ (Attorney Docket No. H0045530) entitled “TWO STEP PRUNING IN A PHD FILTER” filed on even date herewith.

BACKGROUND

The objective of see-and-avoid or sense-and-avoid (SAA) is to provide an unmanned aircraft system (UAS) with the capability to perform self-separation and collision avoidance against all air traffic, with or without active, transponder based collision avoidance systems. SAA requires the UAS to detect and track intruder aircraft in the operating vicinity of the ownship aircraft to identify guidance maneuvers required to perform self-separation and collision avoidance. The detect and track functions are key enablers for UAS SAA capability because the UAS cannot perform self-separation or collision avoidance maneuvers for undetected, untracked intruder aircraft. The detect function refers to using surveillance sensors to measure the position of intruder aircraft relative to the ownship UAS. The track function refers to fusing the surveillance sensor measurements together to estimate the trajectory statistics (also referred to herein as the track) of the intruder aircraft relative to the ownship UAS. The surveillance sensors provide measurements with corresponding measurement IDs that can be correlated across time or random across time.

The track function estimates the tracks of the intruder aircraft using a data association algorithm to assign measurements to a current track, a filter to fuse sensor measurements with the current estimates of the track statistics, and a trajectory manager that oversees the sensor fusion operation, initiates tracks, maintains tracks, and deletes tracks.

One tracking system uses random finite sets (RFS) to track multiple intruder aircraft (IA) for UAS SAA, with the RFS being an implementation of a multi-hypothesis testing (MHT) approach. RFS casts the multiple IA tracking problem into a set-valued state space where the statistics of the set-valued state vector and set-valued measurement vector are approximated using their first-order moments (also referred to herein as an intensity), and applied in a Bayesian filter framework to estimate the IA track statistics using Gaussian mixtures. The resulting filter is referred to as a probabilistic hypothesis density (PHD) filter. An intensity refers to a weight, a state mean vector, and a state covariance matrix of an element of the set-valued state space where this element corresponds to the statistics of a track.

SUMMARY

In one embodiment, a method of tracking multiple objects with a probabilistic hypothesis density filter is provided. The method includes obtaining a plurality of measurements corresponding to a first object with at least one sensor, the at least one sensor providing one or more first track IDs for the plurality of measurements. A T_(k) first track intensity is generated for the first object based on the plurality of measurements, the T_(k) first track intensity including a weight, a state mean vector, and a state covariance matrix of statistics of a track of the first object at time T_(k). A T_(k+1) first predicted intensity is then generated for the first object based on the T_(k) first track intensity, the T_(k+1) first predicted intensity corresponding to time T_(k+1). A T_(k+1) measurement from a first sensor of the at least one sensors is obtained, the first sensor providing a second track ID for the T_(k+1) measurement, wherein the T_(k+1) measurement corresponds to time T_(k+1). The second track ID is compared to the one or more first track IDs, and the T_(k+1) first predicted intensity is selectively updated with the T_(k+1) measurement based on whether the second track ID matches any of the one or more first track IDs to generate a T_(k+1) first measurement-to-track intensity for the first object at time T_(k+1).

DRAWINGS

Understanding that the drawings depict only exemplary embodiments and are not therefore to be considered limiting in scope, the exemplary embodiments will be described with additional specificity and detail through the use of the accompanying drawings, in which:

FIG. 1 is a block diagram of an example environment in which a PHD filter based tracking system may be used.

FIG. 2 is a block diagram of an example tracking system used in the environment of FIG. 1.

FIG. 3 is a flow diagram of an example method for tracking a plurality of objects with the tracking system of FIG. 2.

In accordance with common practice, the various described features are not drawn to scale but are drawn to emphasize specific features relevant to the exemplary embodiments.

DETAILED DESCRIPTION

The subject matter described herein provides for a method of updating intensities that are being tracked in a probabilistic hypothesis density (PHD) filter by using track identifiers (IDs) provided by one or more sensors obtaining object measurements corresponding to the intensities. A track ID is an identifier provided by a sensor, wherein the identifier is correlated across time to a series of measurements. One type of track ID is an international civil aviation organization (ICAO) aircraft address that is transmitted by an aircraft along with corresponding measurement information and is received by a sensor along with the corresponding measurement information. Examples of sensors that are able to receive such ICAO aircraft addresses include an automatic dependent surveillance-broadcast (ADS-B) sensor and a traffic collision avoidance system (TCAS) mode S sensor. Another type of track ID is an identifier from a sensor that correlates measurements over time. In particular, such sensors identify tracks of objects by correlating measurements over time and assigning an ID to those tracks. These IDs are provided by the sensor along with the measurements. Since these IDs are generated by a sensor that correlates its own measurements over time, these IDs are sensor specific. That is, even though a first sensor and a second sensor may be obtaining measurements of the same object, the first sensor and second sensor correlate their own measurements, not the measurements of the other sensor; therefore, the track ID provided by each sensor is different and corresponds to the measurements from that sensor not the other sensor. Examples of a sensor that provides such a track ID for correlated measurements include a TCAS mode C sensor, certain LiDARs, and certain radars. The subject matter described herein utilizes these track IDs to improve the accuracy and efficiency with which multiple objects can be tracked in a PHD filter.

FIG. 1 is a block diagram of an example environment in which a PHD filter based tracking system 102 may be used. In the example shown herein, the tracking system 102 is installed within an aircraft 104, however, the tracking system 102 can be installed within any vehicle or can be a standalone system. The tracking system 102 is configured to detect and track other objects in the environment. In this example, the tracking system 102 is configured to detect objects in the air such as intruder aircraft (IA) 106, 108. In an example, the tracking system 102 is part of a sense-and-avoid (SAA) system and the aircraft 104 is an unmanned aircraft system (UAS).

FIG. 2 is a block diagram of an example tracking system 102. The tracking system 102 includes a plurality of sensors 202-206 configured to detect objects in the environment around the sensors 202-206. The plurality of sensors 202-206 can include any suitable sensor such as a radar 202, TCAS sensor 203, ADS-B sensor 204, optical camera 205, and a LiDAR 206. Other sensors may be used as well. Additionally, any number of sensors including multiple of the same type of sensors may be used. The sensors 202-206 are coupled to one or more processing devices 208. The sensors 202-206 are configured to obtain measurements and send the measurements to the one or more processing devices 208. As mentioned above, some or all of the sensors 202-206 can be configured to send a track ID along with a measurement to the one or more processing devices 208.

The one or more processing devices 208 are configured to track a plurality of objects (such as intruder aircraft 106, 108) based on the measurements received from the sensors 202-206. To track the objects, the one or more processing devices 208 are configured to execute instructions 210 stored on one or more data storage devices 212 coupled to the one or more processing devices 208. The instructions 210, when executed by the one or more processing devices 208, cause the one or more processing devices 208 to implement the actions to track objects based on the measurements from the sensors 202-206. The one or more processing devices 208 can include a central processing unit (CPU), microcontroller, microprocessor, (e.g., a digital signal processor), field programmable gate array (FPGA), application specific integrated circuit (ASIC), or other processing device. In certain examples, the one or more data storage devices 212 include a non-volatile electronic hardware device for storing machine readable data and instructions. In an example, the one or more data storage devices 212 store information on any appropriate computer readable medium used for storage of computer readable instructions or data structures. The computer readable medium can be implemented as any available media that can be accessed by the one or more processing devices 208. Suitable computer readable media may include storage media such as magnetic or optical media. For example, storage media can include a conventional hard disk, Compact Disk-Read Only Memory (CD-ROM), solid state drive (SSD), other flash memory, Read Only Memory (ROM), and Electrically Erasable Programmable ROM (EEPROM). The one or more processing devices 208 are also coupled to memory 214 that is configured to store data and instructions during execution by the one or more processing devices 208. The memory 214 can include volatile or non-volatile media such as Random Access Memory (RAM) (including, but not limited to, Synchronous Dynamic Random Access Memory (SDRAM), Double Data Rate (DDR) RAM, RAMBUS Dynamic RAM (RDRAM), and Static RAM (SRAM), etc.). In an example, the one or more processing devices 208 are configured to output information regarding the tracks of the objects to an output device such as a display device. In some examples, the one or more processing devices 208 provide the track information to a larger SAA system for controlling movement of an unmanned aircraft system.

FIG. 3 is a flow diagram of an example method 300 for tracking a plurality of objects with the tracking system 102. The tracking system 102 implements a loop that computes a plurality of intensities and updates the intensities during each loop based on newly obtained measurements from the sensors 202-206. The loop operates in real time to track a plurality of objects that are measured by the sensors 202-206. As discussed above, the loop implements a probabilistic hypothesis density (PHD) filter to update the intensities. The PHD filter loop attempts to maintain a single intensity for each object being tracked. In the case of a tracking system 102 for an aircraft 104, the PHD filter loop attempts to maintain a single intensity for each intruder aircraft 106, 108, and/or other airborne object within a field-of-view of a sensor 202-206. During a given loop, one or more intensities are maintained corresponding to the number of objects being tracked at that time. Each iteration through the loop updates each intensity being maintained to the next time step unless the particular intensity is deleted (no longer tracked).

The tracking method 300 operates on measurements that have a track ID associated therewith that was provided by a sensor 202-206. Accordingly, one or more measurements and their associated track IDs are provided by the sensors 202-206 (block 302). The one or more measurements each have a single respective track ID associated therewith. In some examples, other measurements that do not have a track ID associated therewith are also obtained by the sensors 202-206. These other measurements can also be used to update intensities maintained by the loop of method 300 in a manner known to those skilled in the art. Actions to update the intensities with such other measurements are not shown in FIG. 3.

The tracking method 300 utilizes the track IDs provided by the sensors 202-206 to determine whether to update a currently maintained intensity with a newly obtained measurement from the sensors 202-206. The tracking method 300 utilizes the fact that the track ID provided by a sensor 202-206 indicates a potential correlation with previous measurements to determine which intensities to update with which measurements. In order to do this, the tracking method 300 associates one or more track IDs with a currently maintained intensity. In some examples, all currently maintained intensities have at least one track ID associated therewith, however, in other examples one or more of the currently maintained intensities may not have a track ID associated therewith. In any case, the intensities that do have a track ID associated therewith can proceed through the method 300 as described herein. Any intensity that does not have a track ID associated therewith can be updated in any suitable manner including in a manner known to those skilled in the art. Actions to update an intensity that does not have a track ID associated therewith are not shown in FIG. 3.

As mentioned above, each loop of method 300 updates each intensity that is not deleted to the next time step. As used herein, time steps are referred to as T_(k), T_(k+1) for the time step which immediately follows time step T_(k), T_(k+2) for the time step which immediately follows time step T_(k+1), etc. The length of time corresponding to a time step can be determined in any suitable manner, such as based on the frequency of measurements provided by one or more of the sensors 202-206. For a given loop of the method 300, the one or more measurements provided by the sensors 202-206 correspond to the time step at which the one or more intensities are being updated. In an example loop, therefore, the one or more intensities input into the loop (block 304) correspond to time step T_(k) and the one or more measurements input into the loop (block 302) correspond to time step T_(k+1). During this iteration of the loop, the one or more intensities are predicted to time step T_(k+1) (block 308) and updated to time step T_(k+1) using the one or more measurements that correspond to time step T_(k+1).

In an example, one or more T_(k) intensities (intensities corresponding to time step T_(k)) are provided (block 304) from the previous iteration of the loop. The one or more T_(k) intensities are the one or more intensities that were output from the previous iteration of the loop. In examples where the tracking system 102 provides tracks of objects to an SAA system, the one or more T_(k) intensities are output to the SAA system as the tracks for time step T_(k). Each intensity progresses through multiple intermediate stages during updating by method 300. An intensity that has completed updating for a given time step and is output (e.g., to an SAA system) is referred to herein as a “track intensity”. Accordingly, the one or more T_(k) intensities input into a loop of method 300 are also referred to herein as one or more T_(k) “track” intensities.

Ignoring any T_(k) track intensities that do not have a track ID associated therewith (as discussed above), each of the one or more T_(k) track intensities input into the loop has a respective one or more track IDs associated therewith. Each of these track IDs corresponds to one or more measurements from a sensor 202-206 that have been used to update (in a previous time step) the respective T_(k) track intensity. The one or more track IDs can correspond to measurements that have been used to update the T_(k) track intensity at any time step including and previous to the T_(k) time step. For example, the respective one or more track IDs can correspond to measurements that have been used to update the corresponding T_(k) track intensity at the T_(k) time step, the T_(k−1) time step, the T_(k−2) time step, etc. More detail regarding the process of associating one or more track IDs with a track intensity is provided below.

In any case, the one or more T_(k) track intensities (block 304) collectively have a first one or more track IDs associated therewith. Similarly, the one or more measurements (block 302) from the sensors 202-206 collectively have a second one or more track IDs provided therewith. The second one or more track IDs are compared with the first one or more track IDs to determine which, if any, T_(k) track intensities to update with which, if any, of the one or more measurements. In an example, to compare the second one or more track IDs with the first one or more track IDs, each track ID from the second one or more track IDs is compared with each track ID from the one or more first track IDs. A match occurs when a track ID from the second one or more track IDs is the same as a track ID from the first one or more track IDs. The one or more T_(k) track intensities are selectively updated based on whether any of the second one or more track IDs match the one or more track IDs of the first one or more track IDs that are associated with a respective T_(k) track intensity. That is, a given T_(k) track intensity is selectively updated based on whether any of the second one or more track IDs match any of the one or more track IDs associated with the given T_(k) track intensity.

In addition to using the comparison between the one or more track IDs to determine whether to update the one or more T_(k) track intensities, a statistical distance test is also used. The statistical distance test includes computing a statistical distance between an intensity and a measurement. Any suitable distance test can be used, such as a Malhanobis distance test. Since the one or more measurements correspond to time step T_(k+1), in order to accurately compute a statistical distance, a predicted intensity for time step T_(k+1) (a T_(k+1) predicted intensity) is computed (block 308) for each of the one or more T_(k+1) track intensities. These one or more T_(k+1) predicted intensities can be computed in any suitable manner including in ways known to those skilled in the art. Once the T_(k+1) predicted intensities are computed, statistical distances can be computed between the one or more T_(k+1) predicted intensities and the one or more measurements respectively. The T_(k+1) predicted intensities are then selectively updated based on whether a corresponding statistical distance (as explained below) is below a threshold. The threshold can be selected in any suitable manner.

In an example, a statistical distance is computed for each pair of the one or more measurements and the T_(k+1) predicted intensities. That is, a statistical distance is computed between each of the one or more measurements and each of the one or more T_(k+1) predicted intensities. If any of the measurement-T_(k+1) predicted intensity pairs have at least one matching track ID and have a statistical distance that is below a threshold, that T_(k+1) predicted intensity is updated with the paired measurement. If there is no matching track ID or the statistical distance is above the threshold for a given measurement-T_(k+1) predicted intensity pair, then that T_(k+1) predicted intensity is not updated with the paired measurement. This analysis is repeated for each measurement-T_(k+1) predicted intensity pair.

In another example, instead of computing the statistical distance for each pair of the one or more measurements and the T_(k+1) predicted intensities, a statistical distance test is selectively computed based on whether any matching track IDs are present for the measurement-T_(k+1) predicted intensity pair. For example, for a given measurement-T_(k+1) predicted intensity pair, if the track ID provided with that measurement matches any of the track IDs associated with the T_(k+1) predicted intensity, then the statistical distance between that measurement and that T_(k+1) predicted intensity are computed. If the statistical distance is below a threshold, that T_(k+1) predicted intensity is updated with the paired measurement. If the statistical distance is above the threshold, then that T_(k+1) predicted intensity if not updated with the paired measurement. If, however, the track ID provided with the measurement does not match any of track IDs associated with the T_(k+1) predicted intensity, then the statistical distance is not computed and that T_(k+1) predicted intensity is not updated with the paired measurement. This analysis is repeated for each measurement-T_(k+1) predicted intensity pair.

In either case, the one or more T_(k+1) predicted intensities are selectively updated with the one or more measurements based on their track IDs and the statistical distances. Updating a T_(k+1) predicted intensity with a measurement (block 310) refers to the process of adjusting the prediction to take into account the measurement. Basically, the analysis of the track IDs and the statistical distance identifies which measurements likely correspond to which T_(k+1) predicted intensities. Since track IDs provide evidence of a correlation between a previous measurement and a current measurement, the track IDs can be used as a simple and effective aid in determining whether a given measurement corresponds to an object being tracked by a given T_(k+1) predicted intensity.

In an example, this updating includes computing a measurement-to-track association between the paired measurement and T_(k+1) predicted intensity to generate a measurement-to-track intensity for the measurement-T_(k+1) predicted intensity pair. Such a measurement-to-track association can be computed in any suitable manner, including in ways know to those skilled in the art. The measurement-to-track intensity corresponds to time step T_(k+1) and, therefore, is also referred to as a T_(k+1) measurement-to-track intensity. In this example, measurement-to-track intensities are generated for each measurement-T_(k+1) predicted intensity pair that has a matching track ID and a statistical distance below the threshold.

In addition to being used to selectively determine whether to update a T_(k+1) predicted intensity, track IDs can also be used to determine whether to initiate a new intensity (block 309). In an example, if a track ID in the second one or more track IDs (provided with the one or more measurements) does not match any of the first one or more track IDs (associated with the one or more T_(k) track intensities), then a new intensity is initiated having values equal to the measurement provided with the (non-matching) track ID. Since the track IDs provide evidence of a correlation between previous measurements and a current measurement, if no current intensities (T_(k) track intensities) have a track ID that matches a track ID of a measurement, this provides evidence that the measurement corresponding to that track ID is a measurement of a newly sensed object by a given sensor. Accordingly, a new intensity is created for that measurement. Such a newly sensed object can be an object that just came into view of the sensor or can occur when a sensor drops an object for a while—for whatever reason—and then picks up the object again. In any case, a new intensity is created for each measurement of the one or more measurements in which the track ID provided therewith does not match any of the first one or more track IDs. The track ID from the measurement used to create the new intensity is associated with that new intensity.

In an example, these one or more new intensities are analyzed in the same manner as the one or more T_(k−1) predicted intensities to determine whether to update the one or more new intensities based on whether each new intensity-measurement pair has a matching track ID and a statistical distance below a threshold (block 310). In this example, since each new intensity has values equal to a measurement and has the track ID from that measurement associated therewith, each new intensity will have one measurement that has a matching track ID and a statistical distance below the threshold. Similar to that described above, updating a new intensity includes computing a measurement-to-track association to generate a measurement-to-track intensity based on the measurement-new intensity pair.

The T_(k+1) predicted intensities, new intensities, and measurement-to-track intensities are then further processed by pruning and merging the intensities to generate the T_(k+1) track intensities for this loop (block 312). Any suitable process of pruning and merging intensities can be used, including processes known to those skilled in the art.

The resulting one or more T_(k+1) track intensities can be output for display and/or further analysis, such as by an SAA system (block 314). The one or more T_(k+1) track intensities are also provided as input into the next iteration of the loop for updating based on one or more measurements for time step T_(k+2).

As mentioned above, in order to utilize track IDs to determine whether to update a track intensity and a new intensity one or more track IDs are associated with the one or more track intensities and one or more new intensities. The one or more track IDs associated with a track intensity correspond to measurements used to update/generate the track intensity. For a new intensity, the track ID associated therewith is the track ID provided with the measurement from which the new intensity was created as discussed above. For a measurement-to-track intensity, the track ID associated therewith is the track ID from the measurement of the one or more measurements in the current time step that was used to update the predicted intensity to generate the measurement-to-track intensity.

For a track intensity, the track intensity maintains all track IDs from any measurement used to create the track intensity. For example, if no intensities are merged with a given track intensity as it is updated to the next time step, the updated track intensity maintains the same track ID(s) as the previous track intensity. If, however, a first intensity is merged (block 312) with a second one or more intensities to create an updated track intensity, the updated track intensity has associated therewith all the track IDs from the first intensity and the second one or more intensities. The first intensity and second one or more intensities can be any type of intensity including a predicted intensity, a measurement-to-track intensity, and a new intensity. Accordingly, if a predicted intensity and a measurement-to-track intensity are merged to form a track intensity, that track intensity has associated therewith all the track ID(s) associated with the predicted intensity and the track ID associated with the measurement-to-track intensity.

If an intensity is pruned (block 312), that intensity is deleted (no longer maintained) and, therefore, is not present in the updated track intensities. Any track IDs associated with a pruned intensity are not passed on to an updated track intensity by the pruned intensity. Finally, if a measurement-to-track intensity is not merged with any other intensities and an updated track intensity is created based on the measurement-to-track intensity, the track ID associated with the measurement-to-track intensity is associated with the updated track intensity. No other track IDs are associated with such an updated track intensity. Similarly, if a new intensity is not merged with any other intensities and an updated track intensity is created based thereon, the track ID associated with the new intensity is associated with the updated track intensity. No other track IDs are associated with such an updated track intensity.

Example Embodiments

Example 1 includes a method of tracking multiple objects with a probabilistic hypothesis density filter, the method comprising: obtaining a plurality of measurements corresponding to a first object with at least one sensor, the at least one sensor providing one or more first track IDs for the plurality of measurements; generating a T_(k) first track intensity for the first object based on the plurality of measurements, the T_(k) first track intensity including a weight, a state mean vector, and a state covariance matrix of statistics of a track of the first object at time T_(k); generating a T_(k+1) first predicted intensity for the first object based on the T_(k) first track intensity, the T_(k+1) first predicted intensity corresponding to time T_(k+1); obtaining a T_(k+1) measurement from a first sensor of the at least one sensors, the first sensor providing a second track ID for the T_(k+1) measurement, wherein the T_(k+1) measurement corresponds to time T_(k+1); comparing the second track ID to the one or more first track IDs; and selectively updating the T_(k+1) first predicted intensity with the T_(k+1) measurement based on whether the second track ID matches any of the one or more first track IDs to generate a T_(k+1) first measurement-to-track intensity for the first object at time T_(k+1).

Example 2 includes the method of Example 1, comprising: computing a statistical distance between the T_(k+1) first predicted intensity and the T_(k+1) measurement; and wherein selectively updating includes selectively updating the T_(k+1) first predicted intensity with the T_(k+1) measurement based on whether the statistical distance is less than a threshold.

Example 3 includes the method of Example 2, wherein selectively updating includes: if the second track ID matches any of the one or more first track IDs and the statistical distance is less than a threshold, updating the T_(k+1) first predicted intensity with the T_(k+1) measurement; and if either the second track ID does not match any of the one or more first track IDs or the statistical distance is greater than the threshold, not updating the T_(k+1) first predicted intensity with the T_(k+1) measurement.

Example 4 includes the method of any of Examples 1-3, comprising: generating a plurality of T_(k) track intensities including the T_(k) first track intensity, the plurality of T_(k) track intensities having a plurality of track IDs associated therewith, the plurality of track IDs including the first one or more track IDs, if the second track ID does not match any of the plurality of track IDs, generating a new intensity having values equal to the T_(k+1) measurement.

Example 5 includes the method of Example 4, comprising: generating a T_(k+1) second track intensity for a second object based on the new intensity, the T_(k+1) second track intensity corresponding to time T_(k+1); generating a T_(k+2) second predicted intensity based on the T_(k+1) second track intensity, the T_(k+2) second predicted intensity corresponding to time T_(k+2); associating the second track ID with the T_(k+2) second predicted intensity; obtaining a T_(k+2) measurement from the first sensor, the first sensor providing a third track ID for the T_(k+2) measurement, wherein the T_(k+2) measurement corresponds to time T_(k+2); comparing the third track ID to the second track ID; computing a second statistical distance between the T_(k+2) second predicted intensity and the T_(k+2) measurement; selectively updating the T_(k+2) second predicted intensity with the T_(k+2) measurement based on whether the third track ID matches the second track ID and based on whether the second statistical distance is less than the threshold to generate a T_(k+2) second measurement-to-track intensity for the second object at time T_(k+2).

Example 6 includes the method of any of Examples 1-5, comprising: generating a T_(k+1) first track intensity based on the T_(k+1) first measurement-to-track intensity; associating the one or more first track IDs with the T_(k+1) first track intensity; generating a T_(k+2) first predicted intensity for the first object based on the T_(k+1) first track intensity, the T_(k+2) first predicted intensity corresponding to time T_(k+2); obtaining a T_(k+2) measurement from the first sensor, the first sensor providing a fourth track ID for the T_(k+2) measurement, wherein the T_(k+2) measurement corresponds to time T_(k+2); comparing the fourth track ID to the one or more first track IDs; and selectively updating the T_(k+2) first predicted intensity with the T_(k+2) measurement based on whether the fourth track ID matches any of the one or more first track IDs to generate a T_(k+2) first track intensity for the first object at time T_(k+2).

Example 7 includes the method of any of Examples 1-6, wherein selectively updating includes: computing a statistical distance between the T_(k+1) first predicted intensity and the T_(k+1) measurement, wherein selectively updating includes, if the second track ID matches any of the one or more first track IDs and the statistical distance is less than a threshold: updating the T_(k+1) first predicted intensity with the T_(k+1) measurement to generate a T_(k+1) first measurement-to-track intensity; and associating only the second track ID of the one or more first track IDs with the T_(k+1) first measurement-to-track intensity; pruning the T_(k+1) first predicted intensity such that the T_(k+1) first predicted intensity is no longer used for tracking the first object; and generating a T_(k+1) track intensity from the T_(k+1) first measurement-to-track intensity; and associating only the second track ID of the one or more first track IDs with the T_(k+1) track intensity.

Example 8 includes the method of any of Examples 1-7, wherein each track ID of the one or more first track IDs and the second track ID is one of an identifier assigned by a sensor to a set of measurements obtained by that sensor that are correlated across time, or an international civil aviation organization (ICAO) aircraft address received by a sensor and corresponding to a respective measurement for that sensor.

Example 9 includes a tracking system comprising: one or more processing devices; and one or more data storage devices including instructions which, when executed by the one or more processing devices, cause the one or more processing devices to track multiple objects with a probabilistic hypothesis density filter, wherein the instructions cause the one or more processing devices to: obtain a plurality of measurements corresponding to a first object with at least one sensor, the at least one sensor providing one or more first track IDs for the plurality of measurements; generate a T_(k) first track intensity for the first object based on the plurality of measurements, the T_(k) first track intensity including a weight, a state mean vector, and a state covariance matrix of statistics of a track of the first object at time T_(k); generate a T_(k+1) first predicted intensity for the first object based on the T_(k) first track intensity, the T_(k+1) first predicted intensity corresponding to time T_(k+1); obtain a T_(k+1) measurement from a first sensor of the at least one sensors, the first sensor providing a second track ID for the T_(k+1) measurement, wherein the T_(k+1) measurement corresponds to time T_(k+1); compare the second track ID to the one or more first track IDs; and selectively update the T_(k−1) first predicted intensity with the T_(k+1) measurement based on whether the second track ID matches any of the one or more first track IDs to generate a T_(k+1) first measurement-to-track intensity for the first object at time T_(k+1).

Example 10 includes the tracking system of Example 9, wherein the instructions cause the one or more processing devices to: compute a statistical distance between the T_(k+1) first predicted intensity and the T_(k+1) measurement; and wherein selectively update includes selectively update the T_(k+1) first predicted intensity with the T_(k+1) measurement based on whether the statistical distance is less than a threshold.

Example 11 includes the tracking system of Example 10, wherein selectively update includes: if the second track ID matches any of the one or more first track IDs and the statistical distance is less than a threshold, update the T_(k+1) first predicted intensity with the T_(k+1) measurement; and if either the second track ID does not match any of the one or more first track IDs or the statistical distance is greater than the threshold, not updating the T_(k+1) first predicted intensity with the T_(k+1) measurement.

Example 12 includes the tracking system of any of Examples 9-11, wherein the instructions cause the one or more processing devices to: generate a plurality of T_(k) track intensities including the T_(k) first track intensity, the plurality of T_(k) track intensities having a plurality of track IDs associated therewith, the plurality of track IDs including the first one or more track IDs, if the second track ID does not match any of the plurality of track IDs, generate a new intensity having values equal to the T_(k+1) measurement.

Example 13 includes the tracking system of Example 12, wherein the instructions cause the one or more processing devices to: generate a T_(k+1) second track intensity for a second object based on the new intensity, the T_(k+1) second track intensity corresponding to time T_(k+1); generate a T_(k+2) second predicted intensity based on the T_(k+1) second track intensity, the T_(k+2) second predicted intensity corresponding to time T_(k+2); associate the second track ID with the T_(k+2) second predicted intensity; obtain a T_(k+2) measurement from the first sensor, the first sensor providing a third track ID for the T_(k+2) measurement, wherein the T_(k+2) measurement corresponds to time T_(k+2); compare the third track ID to the second track ID; compute a second statistical distance between the T_(k+2) second predicted intensity and the T_(k+2) measurement; selectively update the T_(k+2) second predicted intensity with the T_(k+2) measurement based on whether the third track ID matches the second track ID and based on whether the second statistical distance is less than the threshold to generate a T_(k+2) second measurement-to-track intensity for the second object at time T_(k+2).

Example 14 includes the tracking system of any of Examples 9-13, wherein the instructions cause the one or more processing devices to: generate a T_(k+1) first track intensity based on the T_(k+1) first measurement-to-track intensity; associate the one or more first track IDs with the T_(k+1) first track intensity; generate a T_(k+2) first predicted intensity for the first object based on the T_(k+1) first track intensity, the T_(k+2) first predicted intensity corresponding to time T_(k+2); obtain a T_(k+2) measurement from the first sensor, the first sensor providing a fourth track ID for the T_(k+2) measurement, wherein the T_(k+2) measurement corresponds to time T_(k+2); compare the fourth track ID to the one or more first track IDs; and selectively update the T_(k+2) first predicted intensity with the T_(k+2) measurement based on whether the fourth track ID matches any of the one or more first track IDs to generate a T_(k+2) first track intensity for the first object at time T_(k+2).

Example 15 includes the tracking system of any of Examples 9-14, wherein selectively update includes: compute a statistical distance between the T_(k+1) first predicted intensity and the T_(k+1) measurement, wherein selectively update includes, if the second track ID matches any of the one or more first track IDs and the statistical distance is less than a threshold: update the T_(k+1) first predicted intensity with the T_(k+1) measurement to generate a T_(k+1) first measurement-to-track intensity; and associate only the second track ID of the one or more first track IDs with the T_(k+1) first measurement-to-track intensity; prune the T_(k+1) first predicted intensity such that the T_(k+1) first predicted intensity is no longer used for tracking the first object; and generate a T_(k+1) track intensity from the T_(k+1) first measurement-to-track intensity; and associate only the second track ID of the one or more first track IDs with the T_(k+1) track intensity.

Example 16 includes the tracking system of any of Examples 9-15, wherein each track ID of the one or more first track IDs and the second track ID is one of an identifier assigned by a sensor to a set of measurements obtained by that sensor that are correlated across time, or an international civil aviation organization (ICAO) aircraft address received by a sensor and corresponding to a respective measurement for that sensor.

Example 17 includes a computer readable medium including instructions which, when executed by one or more processing devices, cause the one or more processing devices to: obtain a plurality of measurements corresponding to a first object with at least one sensor, the at least one sensor providing one or more first track IDs for the plurality of measurements; generate a T_(k) first track intensity for the first object based on the plurality of measurements, the T_(k) first track intensity including a weight, a state mean vector, and a state covariance matrix of statistics of a track of the first object at time T_(k); generate a T_(k+1) first predicted intensity for the first object based on the T_(k) first track intensity, the T_(k+1) first predicted intensity corresponding to time T_(k+1); obtain a T_(k+1) measurement from a first sensor of the at least one sensors, the first sensor providing a second track ID for the T_(k+1) measurement, wherein the T_(k+1) measurement corresponds to time T_(k+1); compare the second track ID to the one or more first track IDs; and selectively update the T_(k+1) first predicted intensity with the T_(k+1) measurement based on whether the second track ID matches any of the one or more first track IDs to generate a T_(k+1) first measurement-to-track intensity for the first object at time T_(k+1).

Example 18 includes the computer readable medium of Example 17, wherein the instructions cause the one or more processing devices to: compute a statistical distance between the T_(k+1) first predicted intensity and the T_(k+1) measurement; and wherein selectively update includes selectively update the T_(k+1) first predicted intensity with the T_(k+1) measurement based on whether the statistical distance is less than a threshold.

Example 19 includes the computer readable medium of any of Examples 17-18, wherein the instructions cause the one or more processing devices to: generate a plurality of T_(k) track intensities including the T_(k) first track intensity, the plurality of T_(k) track intensities having a plurality of track IDs associated therewith, the plurality of track IDs including the first one or more track IDs, if the second track ID does not match any of the plurality of track IDs, generate a new intensity having values equal to the T_(k+1) measurement.

Example 20 includes the computer readable medium of any of Examples 17-19, wherein each track ID of the one or more first track IDs and the second track ID is one of an identifier assigned by a sensor to a set of measurements obtained by that sensor that are correlated across time, or an international civil aviation organization (ICAO) aircraft address received by a sensor and corresponding to a respective measurement for that sensor. 

What is claimed is:
 1. A method of tracking multiple objects with a probabilistic hypothesis density filter, the method comprising: obtaining a plurality of measurements corresponding to a first object with at least one sensor, the at least one sensor providing one or more first track IDs for the plurality of measurements; generating a T_(k) first track intensity for the first object based on the plurality of measurements, the T_(k) first track intensity including a weight, a state mean vector, and a state covariance matrix of statistics of a track of the first object at time T_(k); generating a T_(k+1) first predicted intensity for the first object based on the T_(k) first track intensity, the T_(k+1) first predicted intensity corresponding to time T_(k+1); obtaining a T_(k+1) measurement from a first sensor of the at least one sensors, the first sensor providing a second track ID for the T_(k+1) measurement, wherein the T_(k+1) measurement corresponds to time T_(k+1); comparing the second track ID to the one or more first track IDs; and selectively updating the T_(k+1) first predicted intensity with the T_(k+1) measurement based on whether the second track ID matches any of the one or more first track IDs to generate a T_(k+1) first measurement-to-track intensity for the first object at time T_(k+1).
 2. The method of claim 1, comprising: computing a statistical distance between the T_(k+1) first predicted intensity and the T_(k+1) measurement; and wherein selectively updating includes selectively updating the T_(k+1) first predicted intensity with the T_(k+1) measurement based on whether the statistical distance is less than a threshold.
 3. The method of claim 2, wherein selectively updating includes: if the second track ID matches any of the one or more first track IDs and the statistical distance is less than a threshold, updating the T_(k+1) first predicted intensity with the T_(k+1) measurement; and if either the second track ID does not match any of the one or more first track IDs or the statistical distance is greater than the threshold, not updating the T_(k+1) first predicted intensity with the T_(k+1) measurement.
 4. The method of claim 1, comprising: generating a plurality of T_(k) track intensities including the T_(k) first track intensity, the plurality of T_(k) track intensities having a plurality of track IDs associated therewith, the plurality of track IDs including the first one or more track IDs, if the second track ID does not match any of the plurality of track IDs, generating a new intensity having values equal to the T_(k+1) measurement.
 5. The method of claim 4, comprising: generating a T_(k+1) second track intensity for a second object based on the new intensity, the T_(k+1) second track intensity corresponding to time T_(k+1); generating a T_(k+2) second predicted intensity based on the T_(k+1) second track intensity, the T_(k+2) second predicted intensity corresponding to time T_(k+2); associating the second track ID with the T_(k+2) second predicted intensity; obtaining a T_(k+2) measurement from the first sensor, the first sensor providing a third track ID for the T_(k+2) measurement, wherein the T_(k+2) measurement corresponds to time T_(k+2); comparing the third track ID to the second track ID; computing a second statistical distance between the T_(k+2) second predicted intensity and the T_(k+2) measurement; selectively updating the T_(k+2) second predicted intensity with the T_(k+2) measurement based on whether the third track ID matches the second track ID and based on whether the second statistical distance is less than the threshold to generate a T_(k+2) second measurement-to-track intensity for the second object at time T_(k+2).
 6. The method of claim 1, comprising: generating a T_(k+1) first track intensity based on the T_(k+1) first measurement-to-track intensity; associating the one or more first track IDs with the T_(k+1) first track intensity; generating a T_(k+2) first predicted intensity for the first object based on the T_(k+1) first track intensity, the T_(k+2) first predicted intensity corresponding to time T_(k+2); obtaining a T_(k+2) measurement from the first sensor, the first sensor providing a fourth track ID for the T_(k+2) measurement, wherein the T_(k+2) measurement corresponds to time T_(k+2); comparing the fourth track ID to the one or more first track IDs; and selectively updating the T_(k+2) first predicted intensity with the T_(k+2) measurement based on whether the fourth track ID matches any of the one or more first track IDs to generate a T_(k+2) first track intensity for the first object at time T_(k+2).
 7. The method of claim 1, wherein selectively updating includes: computing a statistical distance between the T_(k+1) first predicted intensity and the T_(k+1) measurement, wherein selectively updating includes, if the second track ID matches any of the one or more first track IDs and the statistical distance is less than a threshold: updating the T_(k+1) first predicted intensity with the T_(k+1) measurement to generate a T_(k+1) first measurement-to-track intensity; and associating only the second track ID of the one or more first track IDs with the T_(k+1) first measurement-to-track intensity; pruning the T_(k+1) first predicted intensity such that the T_(k+1) first predicted intensity is no longer used for tracking the first object; and generating a T_(k+1) track intensity from the T_(k+1) first measurement-to-track intensity; and associating only the second track ID of the one or more first track IDs with the T_(k+1) track intensity.
 8. The method of claim 1, wherein each track ID of the one or more first track IDs and the second track ID is one of an identifier assigned by a sensor to a set of measurements obtained by that sensor that are correlated across time, or an international civil aviation organization (ICAO) aircraft address received by a sensor and corresponding to a respective measurement for that sensor.
 9. A tracking system comprising: one or more processing devices; and one or more data storage devices including instructions which, when executed by the one or more processing devices, cause the one or more processing devices to track multiple objects with a probabilistic hypothesis density filter, wherein the instructions cause the one or more processing devices to: obtain a plurality of measurements corresponding to a first object with at least one sensor, the at least one sensor providing one or more first track IDs for the plurality of measurements; generate a T_(k) first track intensity for the first object based on the plurality of measurements, the T_(k) first track intensity including a weight, a state mean vector, and a state covariance matrix of statistics of a track of the first object at time T_(k); generate a T_(k+1) first predicted intensity for the first object based on the T_(k) first track intensity, the T_(k+1) first predicted intensity corresponding to time T_(k+1); obtain a T_(k+1) measurement from a first sensor of the at least one sensors, the first sensor providing a second track ID for the T_(k+1) measurement, wherein the T_(k+1) measurement corresponds to time T_(k+1); compare the second track ID to the one or more first track IDs; and selectively update the T_(k+1) first predicted intensity with the T_(k+1) measurement based on whether the second track ID matches any of the one or more first track IDs to generate a T_(k+1) first measurement-to-track intensity for the first object at time T_(k+1).
 10. The tracking system of claim 9, wherein the instructions cause the one or more processing devices to: compute a statistical distance between the T_(k+1) first predicted intensity and the T_(k+1) measurement; and wherein selectively update includes selectively update the T_(k+1) first predicted intensity with the T_(k+1) measurement based on whether the statistical distance is less than a threshold.
 11. The tracking system of claim 10, wherein selectively update includes: if the second track ID matches any of the one or more first track IDs and the statistical distance is less than a threshold, update the T_(k+1) first predicted intensity with the T_(k+1) measurement; and if either the second track ID does not match any of the one or more first track IDs or the statistical distance is greater than the threshold, not updating the T_(k+1) first predicted intensity with the T_(k+1) measurement.
 12. The tracking system of claim 9, wherein the instructions cause the one or more processing devices to: generate a plurality of T_(k) track intensities including the T_(k) first track intensity, the plurality of T_(k) track intensities having a plurality of track IDs associated therewith, the plurality of track IDs including the first one or more track IDs, if the second track ID does not match any of the plurality of track IDs, generate a new intensity having values equal to the T_(k+1) measurement.
 13. The tracking system of claim 12, wherein the instructions cause the one or more processing devices to: generate a T_(k+1) second track intensity for a second object based on the new intensity, the T_(k+1) second track intensity corresponding to time T_(k+1); generate a T_(k+2) second predicted intensity based on the T_(k+1) second track intensity, the T_(k+2) second predicted intensity corresponding to time T_(k+2); associate the second track ID with the T_(k+2) second predicted intensity; obtain a T_(k+2) measurement from the first sensor, the first sensor providing a third track ID for the T_(k+2) measurement, wherein the T_(k+2) measurement corresponds to time T_(k+2); compare the third track ID to the second track ID; compute a second statistical distance between the T_(k+2) second predicted intensity and the T_(k+2) measurement; selectively update the T_(k+2) second predicted intensity with the T_(k+2) measurement based on whether the third track ID matches the second track ID and based on whether the second statistical distance is less than the threshold to generate a T_(k+2) second measurement-to-track intensity for the second object at time T_(k+2).
 14. The tracking system of claim 9, wherein the instructions cause the one or more processing devices to: generate a T_(k+1) first track intensity based on the T_(k+1) first measurement-to-track intensity; associate the one or more first track IDs with the T_(k+1) first track intensity; generate a T_(k+2) first predicted intensity for the first object based on the T_(k+1) first track intensity, the T_(k+2) first predicted intensity corresponding to time T_(k+2); obtain a T_(k+2) measurement from the first sensor, the first sensor providing a fourth track ID for the T_(k+2) measurement, wherein the T_(k+2) measurement corresponds to time T_(k+2); compare the fourth track ID to the one or more first track IDs; and selectively update the T_(k+2) first predicted intensity with the T_(k+2) measurement based on whether the fourth track ID matches any of the one or more first track IDs to generate a T_(k+2) first track intensity for the first object at time T_(k+2).
 15. The tracking system of claim 9, wherein selectively update includes: compute a statistical distance between the T_(k+1) first predicted intensity and the T_(k+1) measurement, wherein selectively update includes, if the second track ID matches any of the one or more first track IDs and the statistical distance is less than a threshold: update the T_(k+1) first predicted intensity with the T_(k+1) measurement to generate a T_(k+1) first measurement-to-track intensity; and associate only the second track ID of the one or more first track IDs with the T_(k+1) first measurement-to-track intensity; prune the T_(k+1) first predicted intensity such that the T_(k+1) first predicted intensity is no longer used for tracking the first object; and generate a T_(k+1) track intensity from the T_(k+1) first measurement-to-track intensity; and associate only the second track ID of the one or more first track IDs with the T_(k+1) track intensity.
 16. The tracking system of claim 9, wherein each track ID of the one or more first track IDs and the second track ID is one of an identifier assigned by a sensor to a set of measurements obtained by that sensor that are correlated across time, or an international civil aviation organization (ICAO) aircraft address received by a sensor and corresponding to a respective measurement for that sensor.
 17. A computer readable medium including instructions which, when executed by one or more processing devices, cause the one or more processing devices to: obtain a plurality of measurements corresponding to a first object with at least one sensor, the at least one sensor providing one or more first track IDs for the plurality of measurements; generate a T_(k) first track intensity for the first object based on the plurality of measurements, the T_(k) first track intensity including a weight, a state mean vector, and a state covariance matrix of statistics of a track of the first object at time T_(k); generate a T_(k+1) first predicted intensity for the first object based on the T_(k) first track intensity, the T_(k+1) first predicted intensity corresponding to time T_(k+1); obtain a T_(k+1) measurement from a first sensor of the at least one sensors, the first sensor providing a second track ID for the T_(k+1) measurement, wherein the T_(k+1) measurement corresponds to time T_(k+1); compare the second track ID to the one or more first track IDs; and selectively update the T_(k+1) first predicted intensity with the T_(k+1) measurement based on whether the second track ID matches any of the one or more first track IDs to generate a T_(k+1) first measurement-to-track intensity for the first object at time T_(k+1).
 18. The computer readable medium of claim 17, wherein the instructions cause the one or more processing devices to: compute a statistical distance between the T_(k+1) first predicted intensity and the T_(k+1) measurement; and wherein selectively update includes selectively update the T_(k+1) first predicted intensity with the T_(k+1) measurement based on whether the statistical distance is less than a threshold.
 19. The computer readable medium of claim 17, wherein the instructions cause the one or more processing devices to: generate a plurality of T_(k) track intensities including the T_(k) first track intensity, the plurality of T_(k) track intensities having a plurality of track IDs associated therewith, the plurality of track IDs including the first one or more track IDs, if the second track ID does not match any of the plurality of track IDs, generate a new intensity having values equal to the T_(k+1) measurement.
 20. The computer readable medium of claim 17, wherein each track ID of the one or more first track IDs and the second track ID is one of an identifier assigned by a sensor to a set of measurements obtained by that sensor that are correlated across time, or an international civil aviation organization (ICAO) aircraft address received by a sensor and corresponding to a respective measurement for that sensor. 